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tutorial11
This tutorial describes the use of iterative linear solvers (AztecOO from the Trilinos project)
with different preconditioners (built-in AztecOO, Ifpack or ML) and corresponding solver options.
Also, the range of Trilins Amesos solver options are shown.
The model is very similar to the model in tutorial 1, except for the different boundary conditions
and that the equations are written in a different way to maximise the number of items around the
diagonal (creating the problem with the diagonally dominant matrix).
These type of systems can be solved using very simple preconditioners such as Jacobi. To do so,
the interoperability with the NumPy package has been exploited and the package itertools used to
iterate through the distribution domains in x and y directions.
The equations are distributed in such a way that the following incidence matrix is obtained:
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The temperature plot (at t=100s, x=0.5, y=*):
.. image:: _static/tutorial11-results.png
:width: 500px
$\mathit{tutorial11}$
BC(left)(00,01)
$\mathit{BC(left)(00,01)}$
$${ { \partial { { \left( { T \left( { 0, 1 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 1 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 1 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,02)
$\mathit{BC(left)(00,02)}$
$${ { \partial { { \left( { T \left( { 0, 2 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 2 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 2 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 2 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,03)
$\mathit{BC(left)(00,03)}$
$${ { \partial { { \left( { T \left( { 0, 3 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 3 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 3 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 3 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,04)
$\mathit{BC(left)(00,04)}$
$${ { \partial { { \left( { T \left( { 0, 4 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 4 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 4 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 4 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,05)
$\mathit{BC(left)(00,05)}$
$${ { \partial { { \left( { T \left( { 0, 5 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 5 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 5 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 5 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,06)
$\mathit{BC(left)(00,06)}$
$${ { \partial { { \left( { T \left( { 0, 6 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 6 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 6 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 6 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,07)
$\mathit{BC(left)(00,07)}$
$${ { \partial { { \left( { T \left( { 0, 7 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 7 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 7 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 7 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,08)
$\mathit{BC(left)(00,08)}$
$${ { \partial { { \left( { T \left( { 0, 8 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 8 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 8 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 8 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,09)
$\mathit{BC(left)(00,09)}$
$${ { \partial { { \left( { T \left( { 0, 9 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 9 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 9 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 9 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,10)
$\mathit{BC(left)(00,10)}$
$${ { \partial { { \left( { T \left( { 0, 10 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 10 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 10 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 10 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,11)
$\mathit{BC(left)(00,11)}$
$${ { \partial { { \left( { T \left( { 0, 11 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 11 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 11 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 11 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,12)
$\mathit{BC(left)(00,12)}$
$${ { \partial { { \left( { T \left( { 0, 12 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 12 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 12 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 12 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,13)
$\mathit{BC(left)(00,13)}$
$${ { \partial { { \left( { T \left( { 0, 13 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 13 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 13 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 13 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,14)
$\mathit{BC(left)(00,14)}$
$${ { \partial { { \left( { T \left( { 0, 14 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 14 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 14 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 14 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,15)
$\mathit{BC(left)(00,15)}$
$${ { \partial { { \left( { T \left( { 0, 15 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 15 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 15 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 15 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,16)
$\mathit{BC(left)(00,16)}$
$${ { \partial { { \left( { T \left( { 0, 16 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 16 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 16 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 16 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,17)
$\mathit{BC(left)(00,17)}$
$${ { \partial { { \left( { T \left( { 0, 17 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 17 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 17 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 17 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,18)
$\mathit{BC(left)(00,18)}$
$${ { \partial { { \left( { T \left( { 0, 18 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 18 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 18 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 18 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,19)
$\mathit{BC(left)(00,19)}$
$${ { \partial { { \left( { T \left( { 0, 19 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 19 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 19 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 19 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(left)(00,20)
$\mathit{BC(left)(00,20)}$
$${ { \partial { { \left( { T \left( { 0, 20 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 0, 20 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 20 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 20 } \right) } } \right) \over \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 0 \right) } } \right) } = 0$$
True
BC(bottom)(01,00)
$\mathit{BC(bottom)(01,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 1, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 1, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(01,01)
$\mathit{HeatBalance(inner)(01,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,02)
$\mathit{HeatBalance(inner)(01,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,03)
$\mathit{HeatBalance(inner)(01,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,04)
$\mathit{HeatBalance(inner)(01,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,05)
$\mathit{HeatBalance(inner)(01,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,06)
$\mathit{HeatBalance(inner)(01,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,07)
$\mathit{HeatBalance(inner)(01,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,08)
$\mathit{HeatBalance(inner)(01,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,09)
$\mathit{HeatBalance(inner)(01,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,10)
$\mathit{HeatBalance(inner)(01,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,11)
$\mathit{HeatBalance(inner)(01,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,12)
$\mathit{HeatBalance(inner)(01,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,13)
$\mathit{HeatBalance(inner)(01,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,14)
$\mathit{HeatBalance(inner)(01,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,15)
$\mathit{HeatBalance(inner)(01,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,16)
$\mathit{HeatBalance(inner)(01,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,17)
$\mathit{HeatBalance(inner)(01,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,18)
$\mathit{HeatBalance(inner)(01,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(01,19)
$\mathit{HeatBalance(inner)(01,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 1, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 1, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 1, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 2, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 0, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) \cdot \left( { { tutorial11.x \left( 1 \right) } - { tutorial11.x \left( 0 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 1, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 1, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(01,20)
$\mathit{BC(top)(01,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 1, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 1, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 1, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(02,00)
$\mathit{BC(bottom)(02,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 2, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 2, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 2, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(02,01)
$\mathit{HeatBalance(inner)(02,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,02)
$\mathit{HeatBalance(inner)(02,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,03)
$\mathit{HeatBalance(inner)(02,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,04)
$\mathit{HeatBalance(inner)(02,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,05)
$\mathit{HeatBalance(inner)(02,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,06)
$\mathit{HeatBalance(inner)(02,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,07)
$\mathit{HeatBalance(inner)(02,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,08)
$\mathit{HeatBalance(inner)(02,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,09)
$\mathit{HeatBalance(inner)(02,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,10)
$\mathit{HeatBalance(inner)(02,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,11)
$\mathit{HeatBalance(inner)(02,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,12)
$\mathit{HeatBalance(inner)(02,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,13)
$\mathit{HeatBalance(inner)(02,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,14)
$\mathit{HeatBalance(inner)(02,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,15)
$\mathit{HeatBalance(inner)(02,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,16)
$\mathit{HeatBalance(inner)(02,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,17)
$\mathit{HeatBalance(inner)(02,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,18)
$\mathit{HeatBalance(inner)(02,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(02,19)
$\mathit{HeatBalance(inner)(02,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 2, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 2, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 2, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 3, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 1, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) \cdot \left( { { tutorial11.x \left( 2 \right) } - { tutorial11.x \left( 1 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 2, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 2, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(02,20)
$\mathit{BC(top)(02,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 2, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 2, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 2, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(03,00)
$\mathit{BC(bottom)(03,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 3, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 3, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 3, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(03,01)
$\mathit{HeatBalance(inner)(03,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,02)
$\mathit{HeatBalance(inner)(03,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,03)
$\mathit{HeatBalance(inner)(03,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,04)
$\mathit{HeatBalance(inner)(03,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,05)
$\mathit{HeatBalance(inner)(03,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,06)
$\mathit{HeatBalance(inner)(03,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,07)
$\mathit{HeatBalance(inner)(03,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,08)
$\mathit{HeatBalance(inner)(03,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,09)
$\mathit{HeatBalance(inner)(03,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,10)
$\mathit{HeatBalance(inner)(03,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,11)
$\mathit{HeatBalance(inner)(03,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,12)
$\mathit{HeatBalance(inner)(03,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,13)
$\mathit{HeatBalance(inner)(03,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,14)
$\mathit{HeatBalance(inner)(03,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,15)
$\mathit{HeatBalance(inner)(03,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,16)
$\mathit{HeatBalance(inner)(03,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,17)
$\mathit{HeatBalance(inner)(03,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,18)
$\mathit{HeatBalance(inner)(03,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(03,19)
$\mathit{HeatBalance(inner)(03,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 3, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 3, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 3, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 4, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 2, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) \cdot \left( { { tutorial11.x \left( 3 \right) } - { tutorial11.x \left( 2 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 3, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 3, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(03,20)
$\mathit{BC(top)(03,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 3, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 3, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 3, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(04,00)
$\mathit{BC(bottom)(04,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 4, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 4, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 4, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(04,01)
$\mathit{HeatBalance(inner)(04,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,02)
$\mathit{HeatBalance(inner)(04,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,03)
$\mathit{HeatBalance(inner)(04,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,04)
$\mathit{HeatBalance(inner)(04,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,05)
$\mathit{HeatBalance(inner)(04,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,06)
$\mathit{HeatBalance(inner)(04,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,07)
$\mathit{HeatBalance(inner)(04,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,08)
$\mathit{HeatBalance(inner)(04,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,09)
$\mathit{HeatBalance(inner)(04,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,10)
$\mathit{HeatBalance(inner)(04,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,11)
$\mathit{HeatBalance(inner)(04,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,12)
$\mathit{HeatBalance(inner)(04,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,13)
$\mathit{HeatBalance(inner)(04,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,14)
$\mathit{HeatBalance(inner)(04,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,15)
$\mathit{HeatBalance(inner)(04,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,16)
$\mathit{HeatBalance(inner)(04,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,17)
$\mathit{HeatBalance(inner)(04,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,18)
$\mathit{HeatBalance(inner)(04,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(04,19)
$\mathit{HeatBalance(inner)(04,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 4, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 4, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 4, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 5, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 3, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) \cdot \left( { { tutorial11.x \left( 4 \right) } - { tutorial11.x \left( 3 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 4, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 4, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(04,20)
$\mathit{BC(top)(04,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 4, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 4, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 4, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(05,00)
$\mathit{BC(bottom)(05,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 5, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 5, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 5, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(05,01)
$\mathit{HeatBalance(inner)(05,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,02)
$\mathit{HeatBalance(inner)(05,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,03)
$\mathit{HeatBalance(inner)(05,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,04)
$\mathit{HeatBalance(inner)(05,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,05)
$\mathit{HeatBalance(inner)(05,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,06)
$\mathit{HeatBalance(inner)(05,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,07)
$\mathit{HeatBalance(inner)(05,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,08)
$\mathit{HeatBalance(inner)(05,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,09)
$\mathit{HeatBalance(inner)(05,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,10)
$\mathit{HeatBalance(inner)(05,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,11)
$\mathit{HeatBalance(inner)(05,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,12)
$\mathit{HeatBalance(inner)(05,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,13)
$\mathit{HeatBalance(inner)(05,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,14)
$\mathit{HeatBalance(inner)(05,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,15)
$\mathit{HeatBalance(inner)(05,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,16)
$\mathit{HeatBalance(inner)(05,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,17)
$\mathit{HeatBalance(inner)(05,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,18)
$\mathit{HeatBalance(inner)(05,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(05,19)
$\mathit{HeatBalance(inner)(05,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 5, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 5, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 5, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 6, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 4, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) \cdot \left( { { tutorial11.x \left( 5 \right) } - { tutorial11.x \left( 4 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 5, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 5, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(05,20)
$\mathit{BC(top)(05,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 5, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 5, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 5, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(06,00)
$\mathit{BC(bottom)(06,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 6, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 6, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 6, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(06,01)
$\mathit{HeatBalance(inner)(06,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,02)
$\mathit{HeatBalance(inner)(06,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,03)
$\mathit{HeatBalance(inner)(06,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,04)
$\mathit{HeatBalance(inner)(06,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,05)
$\mathit{HeatBalance(inner)(06,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,06)
$\mathit{HeatBalance(inner)(06,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,07)
$\mathit{HeatBalance(inner)(06,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,08)
$\mathit{HeatBalance(inner)(06,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,09)
$\mathit{HeatBalance(inner)(06,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,10)
$\mathit{HeatBalance(inner)(06,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,11)
$\mathit{HeatBalance(inner)(06,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,12)
$\mathit{HeatBalance(inner)(06,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,13)
$\mathit{HeatBalance(inner)(06,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,14)
$\mathit{HeatBalance(inner)(06,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,15)
$\mathit{HeatBalance(inner)(06,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,16)
$\mathit{HeatBalance(inner)(06,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,17)
$\mathit{HeatBalance(inner)(06,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,18)
$\mathit{HeatBalance(inner)(06,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(06,19)
$\mathit{HeatBalance(inner)(06,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 6, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 6, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 6, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 7, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 5, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) \cdot \left( { { tutorial11.x \left( 6 \right) } - { tutorial11.x \left( 5 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 6, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 6, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(06,20)
$\mathit{BC(top)(06,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 6, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 6, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 6, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(07,00)
$\mathit{BC(bottom)(07,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 7, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 7, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 7, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(07,01)
$\mathit{HeatBalance(inner)(07,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,02)
$\mathit{HeatBalance(inner)(07,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,03)
$\mathit{HeatBalance(inner)(07,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,04)
$\mathit{HeatBalance(inner)(07,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,05)
$\mathit{HeatBalance(inner)(07,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,06)
$\mathit{HeatBalance(inner)(07,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,07)
$\mathit{HeatBalance(inner)(07,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,08)
$\mathit{HeatBalance(inner)(07,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,09)
$\mathit{HeatBalance(inner)(07,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,10)
$\mathit{HeatBalance(inner)(07,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,11)
$\mathit{HeatBalance(inner)(07,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,12)
$\mathit{HeatBalance(inner)(07,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,13)
$\mathit{HeatBalance(inner)(07,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,14)
$\mathit{HeatBalance(inner)(07,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,15)
$\mathit{HeatBalance(inner)(07,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,16)
$\mathit{HeatBalance(inner)(07,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,17)
$\mathit{HeatBalance(inner)(07,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,18)
$\mathit{HeatBalance(inner)(07,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(07,19)
$\mathit{HeatBalance(inner)(07,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 7, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 7, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 7, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 8, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 6, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) \cdot \left( { { tutorial11.x \left( 7 \right) } - { tutorial11.x \left( 6 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 7, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 7, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(07,20)
$\mathit{BC(top)(07,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 7, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 7, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 7, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(08,00)
$\mathit{BC(bottom)(08,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 8, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 8, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 8, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(08,01)
$\mathit{HeatBalance(inner)(08,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,02)
$\mathit{HeatBalance(inner)(08,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,03)
$\mathit{HeatBalance(inner)(08,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,04)
$\mathit{HeatBalance(inner)(08,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,05)
$\mathit{HeatBalance(inner)(08,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,06)
$\mathit{HeatBalance(inner)(08,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,07)
$\mathit{HeatBalance(inner)(08,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,08)
$\mathit{HeatBalance(inner)(08,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,09)
$\mathit{HeatBalance(inner)(08,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,10)
$\mathit{HeatBalance(inner)(08,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,11)
$\mathit{HeatBalance(inner)(08,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,12)
$\mathit{HeatBalance(inner)(08,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,13)
$\mathit{HeatBalance(inner)(08,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,14)
$\mathit{HeatBalance(inner)(08,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,15)
$\mathit{HeatBalance(inner)(08,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,16)
$\mathit{HeatBalance(inner)(08,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,17)
$\mathit{HeatBalance(inner)(08,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,18)
$\mathit{HeatBalance(inner)(08,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(08,19)
$\mathit{HeatBalance(inner)(08,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 8, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 8, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 8, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 9, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 7, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) \cdot \left( { { tutorial11.x \left( 8 \right) } - { tutorial11.x \left( 7 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 8, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 8, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(08,20)
$\mathit{BC(top)(08,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 8, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 8, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 8, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(09,00)
$\mathit{BC(bottom)(09,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 9, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 9, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 9, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(09,01)
$\mathit{HeatBalance(inner)(09,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,02)
$\mathit{HeatBalance(inner)(09,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,03)
$\mathit{HeatBalance(inner)(09,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,04)
$\mathit{HeatBalance(inner)(09,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,05)
$\mathit{HeatBalance(inner)(09,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,06)
$\mathit{HeatBalance(inner)(09,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,07)
$\mathit{HeatBalance(inner)(09,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,08)
$\mathit{HeatBalance(inner)(09,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,09)
$\mathit{HeatBalance(inner)(09,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,10)
$\mathit{HeatBalance(inner)(09,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,11)
$\mathit{HeatBalance(inner)(09,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,12)
$\mathit{HeatBalance(inner)(09,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,13)
$\mathit{HeatBalance(inner)(09,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,14)
$\mathit{HeatBalance(inner)(09,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,15)
$\mathit{HeatBalance(inner)(09,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,16)
$\mathit{HeatBalance(inner)(09,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,17)
$\mathit{HeatBalance(inner)(09,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,18)
$\mathit{HeatBalance(inner)(09,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(09,19)
$\mathit{HeatBalance(inner)(09,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 9, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 9, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 9, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 10, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 8, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) \cdot \left( { { tutorial11.x \left( 9 \right) } - { tutorial11.x \left( 8 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 9, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 9, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(09,20)
$\mathit{BC(top)(09,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 9, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 9, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 9, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(10,00)
$\mathit{BC(bottom)(10,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 10, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 10, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 10, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(10,01)
$\mathit{HeatBalance(inner)(10,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,02)
$\mathit{HeatBalance(inner)(10,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,03)
$\mathit{HeatBalance(inner)(10,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,04)
$\mathit{HeatBalance(inner)(10,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,05)
$\mathit{HeatBalance(inner)(10,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,06)
$\mathit{HeatBalance(inner)(10,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,07)
$\mathit{HeatBalance(inner)(10,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,08)
$\mathit{HeatBalance(inner)(10,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,09)
$\mathit{HeatBalance(inner)(10,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,10)
$\mathit{HeatBalance(inner)(10,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,11)
$\mathit{HeatBalance(inner)(10,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,12)
$\mathit{HeatBalance(inner)(10,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,13)
$\mathit{HeatBalance(inner)(10,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,14)
$\mathit{HeatBalance(inner)(10,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,15)
$\mathit{HeatBalance(inner)(10,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,16)
$\mathit{HeatBalance(inner)(10,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,17)
$\mathit{HeatBalance(inner)(10,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,18)
$\mathit{HeatBalance(inner)(10,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(10,19)
$\mathit{HeatBalance(inner)(10,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 10, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 10, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 10, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 11, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 9, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) \cdot \left( { { tutorial11.x \left( 10 \right) } - { tutorial11.x \left( 9 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 10, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 10, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(10,20)
$\mathit{BC(top)(10,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 10, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 10, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 10, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(11,00)
$\mathit{BC(bottom)(11,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 11, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 11, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 11, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(11,01)
$\mathit{HeatBalance(inner)(11,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,02)
$\mathit{HeatBalance(inner)(11,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,03)
$\mathit{HeatBalance(inner)(11,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,04)
$\mathit{HeatBalance(inner)(11,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,05)
$\mathit{HeatBalance(inner)(11,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,06)
$\mathit{HeatBalance(inner)(11,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,07)
$\mathit{HeatBalance(inner)(11,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,08)
$\mathit{HeatBalance(inner)(11,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,09)
$\mathit{HeatBalance(inner)(11,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,10)
$\mathit{HeatBalance(inner)(11,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,11)
$\mathit{HeatBalance(inner)(11,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,12)
$\mathit{HeatBalance(inner)(11,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,13)
$\mathit{HeatBalance(inner)(11,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,14)
$\mathit{HeatBalance(inner)(11,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,15)
$\mathit{HeatBalance(inner)(11,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,16)
$\mathit{HeatBalance(inner)(11,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,17)
$\mathit{HeatBalance(inner)(11,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,18)
$\mathit{HeatBalance(inner)(11,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(11,19)
$\mathit{HeatBalance(inner)(11,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 11, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 11, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 11, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 12, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 10, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) \cdot \left( { { tutorial11.x \left( 11 \right) } - { tutorial11.x \left( 10 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 11, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 11, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(11,20)
$\mathit{BC(top)(11,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 11, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 11, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 11, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(12,00)
$\mathit{BC(bottom)(12,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 12, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 12, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 12, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(12,01)
$\mathit{HeatBalance(inner)(12,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,02)
$\mathit{HeatBalance(inner)(12,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,03)
$\mathit{HeatBalance(inner)(12,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,04)
$\mathit{HeatBalance(inner)(12,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,05)
$\mathit{HeatBalance(inner)(12,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,06)
$\mathit{HeatBalance(inner)(12,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,07)
$\mathit{HeatBalance(inner)(12,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,08)
$\mathit{HeatBalance(inner)(12,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,09)
$\mathit{HeatBalance(inner)(12,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,10)
$\mathit{HeatBalance(inner)(12,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,11)
$\mathit{HeatBalance(inner)(12,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,12)
$\mathit{HeatBalance(inner)(12,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,13)
$\mathit{HeatBalance(inner)(12,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,14)
$\mathit{HeatBalance(inner)(12,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,15)
$\mathit{HeatBalance(inner)(12,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,16)
$\mathit{HeatBalance(inner)(12,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,17)
$\mathit{HeatBalance(inner)(12,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,18)
$\mathit{HeatBalance(inner)(12,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(12,19)
$\mathit{HeatBalance(inner)(12,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 12, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 12, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 12, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 13, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 11, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) \cdot \left( { { tutorial11.x \left( 12 \right) } - { tutorial11.x \left( 11 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 12, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 12, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(12,20)
$\mathit{BC(top)(12,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 12, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 12, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 12, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(13,00)
$\mathit{BC(bottom)(13,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 13, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 13, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 13, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(13,01)
$\mathit{HeatBalance(inner)(13,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,02)
$\mathit{HeatBalance(inner)(13,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,03)
$\mathit{HeatBalance(inner)(13,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,04)
$\mathit{HeatBalance(inner)(13,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,05)
$\mathit{HeatBalance(inner)(13,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,06)
$\mathit{HeatBalance(inner)(13,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,07)
$\mathit{HeatBalance(inner)(13,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,08)
$\mathit{HeatBalance(inner)(13,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,09)
$\mathit{HeatBalance(inner)(13,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,10)
$\mathit{HeatBalance(inner)(13,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,11)
$\mathit{HeatBalance(inner)(13,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,12)
$\mathit{HeatBalance(inner)(13,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,13)
$\mathit{HeatBalance(inner)(13,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,14)
$\mathit{HeatBalance(inner)(13,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,15)
$\mathit{HeatBalance(inner)(13,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,16)
$\mathit{HeatBalance(inner)(13,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,17)
$\mathit{HeatBalance(inner)(13,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,18)
$\mathit{HeatBalance(inner)(13,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(13,19)
$\mathit{HeatBalance(inner)(13,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 13, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 13, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 13, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 14, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 12, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) \cdot \left( { { tutorial11.x \left( 13 \right) } - { tutorial11.x \left( 12 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 13, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 13, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(13,20)
$\mathit{BC(top)(13,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 13, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 13, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 13, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(14,00)
$\mathit{BC(bottom)(14,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 14, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 14, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 14, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(14,01)
$\mathit{HeatBalance(inner)(14,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,02)
$\mathit{HeatBalance(inner)(14,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,03)
$\mathit{HeatBalance(inner)(14,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,04)
$\mathit{HeatBalance(inner)(14,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,05)
$\mathit{HeatBalance(inner)(14,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,06)
$\mathit{HeatBalance(inner)(14,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,07)
$\mathit{HeatBalance(inner)(14,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,08)
$\mathit{HeatBalance(inner)(14,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,09)
$\mathit{HeatBalance(inner)(14,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,10)
$\mathit{HeatBalance(inner)(14,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,11)
$\mathit{HeatBalance(inner)(14,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,12)
$\mathit{HeatBalance(inner)(14,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,13)
$\mathit{HeatBalance(inner)(14,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,14)
$\mathit{HeatBalance(inner)(14,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,15)
$\mathit{HeatBalance(inner)(14,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,16)
$\mathit{HeatBalance(inner)(14,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,17)
$\mathit{HeatBalance(inner)(14,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,18)
$\mathit{HeatBalance(inner)(14,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(14,19)
$\mathit{HeatBalance(inner)(14,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 14, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 14, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 14, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 15, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 13, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) \cdot \left( { { tutorial11.x \left( 14 \right) } - { tutorial11.x \left( 13 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 14, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 14, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(14,20)
$\mathit{BC(top)(14,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 14, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 14, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 14, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(15,00)
$\mathit{BC(bottom)(15,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 15, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 15, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 15, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(15,01)
$\mathit{HeatBalance(inner)(15,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,02)
$\mathit{HeatBalance(inner)(15,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,03)
$\mathit{HeatBalance(inner)(15,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,04)
$\mathit{HeatBalance(inner)(15,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,05)
$\mathit{HeatBalance(inner)(15,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,06)
$\mathit{HeatBalance(inner)(15,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,07)
$\mathit{HeatBalance(inner)(15,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,08)
$\mathit{HeatBalance(inner)(15,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,09)
$\mathit{HeatBalance(inner)(15,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,10)
$\mathit{HeatBalance(inner)(15,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,11)
$\mathit{HeatBalance(inner)(15,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,12)
$\mathit{HeatBalance(inner)(15,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,13)
$\mathit{HeatBalance(inner)(15,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,14)
$\mathit{HeatBalance(inner)(15,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,15)
$\mathit{HeatBalance(inner)(15,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,16)
$\mathit{HeatBalance(inner)(15,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,17)
$\mathit{HeatBalance(inner)(15,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,18)
$\mathit{HeatBalance(inner)(15,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(15,19)
$\mathit{HeatBalance(inner)(15,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 15, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 15, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 15, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 16, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 14, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) \cdot \left( { { tutorial11.x \left( 15 \right) } - { tutorial11.x \left( 14 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 15, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 15, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(15,20)
$\mathit{BC(top)(15,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 15, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 15, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 15, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(16,00)
$\mathit{BC(bottom)(16,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 16, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 16, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 16, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(16,01)
$\mathit{HeatBalance(inner)(16,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,02)
$\mathit{HeatBalance(inner)(16,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,03)
$\mathit{HeatBalance(inner)(16,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,04)
$\mathit{HeatBalance(inner)(16,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,05)
$\mathit{HeatBalance(inner)(16,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,06)
$\mathit{HeatBalance(inner)(16,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,07)
$\mathit{HeatBalance(inner)(16,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,08)
$\mathit{HeatBalance(inner)(16,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,09)
$\mathit{HeatBalance(inner)(16,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,10)
$\mathit{HeatBalance(inner)(16,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,11)
$\mathit{HeatBalance(inner)(16,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,12)
$\mathit{HeatBalance(inner)(16,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,13)
$\mathit{HeatBalance(inner)(16,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,14)
$\mathit{HeatBalance(inner)(16,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,15)
$\mathit{HeatBalance(inner)(16,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,16)
$\mathit{HeatBalance(inner)(16,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,17)
$\mathit{HeatBalance(inner)(16,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,18)
$\mathit{HeatBalance(inner)(16,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(16,19)
$\mathit{HeatBalance(inner)(16,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 16, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 16, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 16, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 17, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 15, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) \cdot \left( { { tutorial11.x \left( 16 \right) } - { tutorial11.x \left( 15 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 16, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 16, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(16,20)
$\mathit{BC(top)(16,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 16, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 16, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 16, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(17,00)
$\mathit{BC(bottom)(17,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 17, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 17, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 17, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(17,01)
$\mathit{HeatBalance(inner)(17,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,02)
$\mathit{HeatBalance(inner)(17,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,03)
$\mathit{HeatBalance(inner)(17,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,04)
$\mathit{HeatBalance(inner)(17,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,05)
$\mathit{HeatBalance(inner)(17,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,06)
$\mathit{HeatBalance(inner)(17,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,07)
$\mathit{HeatBalance(inner)(17,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,08)
$\mathit{HeatBalance(inner)(17,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,09)
$\mathit{HeatBalance(inner)(17,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,10)
$\mathit{HeatBalance(inner)(17,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,11)
$\mathit{HeatBalance(inner)(17,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,12)
$\mathit{HeatBalance(inner)(17,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,13)
$\mathit{HeatBalance(inner)(17,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,14)
$\mathit{HeatBalance(inner)(17,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,15)
$\mathit{HeatBalance(inner)(17,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,16)
$\mathit{HeatBalance(inner)(17,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,17)
$\mathit{HeatBalance(inner)(17,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,18)
$\mathit{HeatBalance(inner)(17,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(17,19)
$\mathit{HeatBalance(inner)(17,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 17, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 17, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 17, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 18, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 16, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) \cdot \left( { { tutorial11.x \left( 17 \right) } - { tutorial11.x \left( 16 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 17, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 17, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(17,20)
$\mathit{BC(top)(17,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 17, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 17, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 17, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(18,00)
$\mathit{BC(bottom)(18,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 18, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 18, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 18, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(18,01)
$\mathit{HeatBalance(inner)(18,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,02)
$\mathit{HeatBalance(inner)(18,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,03)
$\mathit{HeatBalance(inner)(18,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,04)
$\mathit{HeatBalance(inner)(18,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,05)
$\mathit{HeatBalance(inner)(18,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,06)
$\mathit{HeatBalance(inner)(18,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,07)
$\mathit{HeatBalance(inner)(18,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,08)
$\mathit{HeatBalance(inner)(18,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,09)
$\mathit{HeatBalance(inner)(18,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,10)
$\mathit{HeatBalance(inner)(18,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,11)
$\mathit{HeatBalance(inner)(18,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,12)
$\mathit{HeatBalance(inner)(18,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,13)
$\mathit{HeatBalance(inner)(18,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,14)
$\mathit{HeatBalance(inner)(18,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,15)
$\mathit{HeatBalance(inner)(18,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,16)
$\mathit{HeatBalance(inner)(18,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,17)
$\mathit{HeatBalance(inner)(18,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,18)
$\mathit{HeatBalance(inner)(18,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(18,19)
$\mathit{HeatBalance(inner)(18,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 18, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 18, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 18, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 19, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 17, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) \cdot \left( { { tutorial11.x \left( 18 \right) } - { tutorial11.x \left( 17 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 18, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 18, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(18,20)
$\mathit{BC(top)(18,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 18, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 18, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 18, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(bottom)(19,00)
$\mathit{BC(bottom)(19,00)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 0 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {-3 {}} \cdot { tutorial11.T \left( { 19, 0 } \right) } } \right) + \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 1 } \right) } } \right) } \right) - { tutorial11.T \left( { 19, 2 } \right) } } \right) \over \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) - { tutorial11.Q_b } } = 0$$
True
HeatBalance(inner)(19,01)
$\mathit{HeatBalance(inner)(19,01)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 1 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 1 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 1 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 1} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 1 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 0 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) \cdot \left( { { tutorial11.y \left( 1 \right) } - { tutorial11.y \left( 0 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,02)
$\mathit{HeatBalance(inner)(19,02)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 2 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 2 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 2 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 2} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 2 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 1 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) \cdot \left( { { tutorial11.y \left( 2 \right) } - { tutorial11.y \left( 1 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,03)
$\mathit{HeatBalance(inner)(19,03)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 3 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 3 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 3 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 3} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 3 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 2 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) \cdot \left( { { tutorial11.y \left( 3 \right) } - { tutorial11.y \left( 2 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,04)
$\mathit{HeatBalance(inner)(19,04)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 4 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 4 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 4 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 4} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 4 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 3 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) \cdot \left( { { tutorial11.y \left( 4 \right) } - { tutorial11.y \left( 3 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,05)
$\mathit{HeatBalance(inner)(19,05)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 5 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 5 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 5 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 5} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 5 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 4 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) \cdot \left( { { tutorial11.y \left( 5 \right) } - { tutorial11.y \left( 4 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,06)
$\mathit{HeatBalance(inner)(19,06)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 6 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 6 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 6 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 6} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 6 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 5 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) \cdot \left( { { tutorial11.y \left( 6 \right) } - { tutorial11.y \left( 5 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,07)
$\mathit{HeatBalance(inner)(19,07)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 7 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 7 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 7 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 7} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 7 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 6 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) \cdot \left( { { tutorial11.y \left( 7 \right) } - { tutorial11.y \left( 6 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,08)
$\mathit{HeatBalance(inner)(19,08)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 8 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 8 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 8 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 8} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 8 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 7 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) \cdot \left( { { tutorial11.y \left( 8 \right) } - { tutorial11.y \left( 7 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,09)
$\mathit{HeatBalance(inner)(19,09)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 9 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 9 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 9 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 9} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 9 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 8 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) \cdot \left( { { tutorial11.y \left( 9 \right) } - { tutorial11.y \left( 8 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,10)
$\mathit{HeatBalance(inner)(19,10)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 10 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 10 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 10 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 10} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 10 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 9 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) \cdot \left( { { tutorial11.y \left( 10 \right) } - { tutorial11.y \left( 9 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,11)
$\mathit{HeatBalance(inner)(19,11)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 11 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 11 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 11 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 11} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 11 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 10 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) \cdot \left( { { tutorial11.y \left( 11 \right) } - { tutorial11.y \left( 10 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,12)
$\mathit{HeatBalance(inner)(19,12)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 12 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 12 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 12 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 12} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 12 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 11 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) \cdot \left( { { tutorial11.y \left( 12 \right) } - { tutorial11.y \left( 11 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,13)
$\mathit{HeatBalance(inner)(19,13)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 13 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 13 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 13 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 13} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 13 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 12 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) \cdot \left( { { tutorial11.y \left( 13 \right) } - { tutorial11.y \left( 12 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,14)
$\mathit{HeatBalance(inner)(19,14)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 14 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 14 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 14 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 14} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 14 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 13 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) \cdot \left( { { tutorial11.y \left( 14 \right) } - { tutorial11.y \left( 13 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,15)
$\mathit{HeatBalance(inner)(19,15)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 15 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 15 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 15 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 15} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 15 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 14 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) \cdot \left( { { tutorial11.y \left( 15 \right) } - { tutorial11.y \left( 14 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,16)
$\mathit{HeatBalance(inner)(19,16)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 16 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 16 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 16 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 16} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 16 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 15 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) \cdot \left( { { tutorial11.y \left( 16 \right) } - { tutorial11.y \left( 15 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,17)
$\mathit{HeatBalance(inner)(19,17)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 17 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 17 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 17 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 17} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 17 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 16 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) \cdot \left( { { tutorial11.y \left( 17 \right) } - { tutorial11.y \left( 16 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,18)
$\mathit{HeatBalance(inner)(19,18)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 18 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 18 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 18 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 18} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 18 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 17 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) \cdot \left( { { tutorial11.y \left( 18 \right) } - { tutorial11.y \left( 17 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
HeatBalance(inner)(19,19)
$\mathit{HeatBalance(inner)(19,19)}$
$${ \left( { \left( { { \rho } \cdot { c_p } } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 19 } \right) } \right) } } } \over { \partial { t } } } \right) } \right) - \left( { { \lambda_p } \cdot \left( { \left( { { \partial { ^2 { \left( { T \left( { 19, 19 } \right) } \right) } } } \over { \partial {x ^2} } } \right) + \left( { { \partial { ^2 { \left( { T \left( { 19, 19 } \right) } \right) } } } \over { \partial {y ^2} } } \right) } \right) } \right) } = 0$$
$${ \left( { \left( { { tutorial11.\rho } \cdot { tutorial11.c_p } } \right) \cdot { { \partial { { tutorial11.T \left( { 19, 19} \right) } } } \over { \partial { t } } } } \right) - \left( { { tutorial11.\lambda_p } \cdot \left( { \left( { \left( { \left( { { tutorial11.T \left( { 20, 19 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 19 } \right) } } \right) \over \left( { \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 19 \right) } } \right) \cdot \left( { { tutorial11.x \left( 19 \right) } - { tutorial11.x \left( 18 \right) } } \right) } \right) } \right) + \left( { \left( { \left( { { tutorial11.T \left( { 19, 20 } \right) } - \left( { {2 {}} \cdot { tutorial11.T \left( { 19, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 18 } \right) } } \right) \over \left( { \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 19 \right) } } \right) \cdot \left( { { tutorial11.y \left( 19 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) } \right) } \right) } = 0$$
False
BC(top)(19,20)
$\mathit{BC(top)(19,20)}$
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { 19, 20 } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0$$
$${ \left( { \left( { \left( - { tutorial11.\lambda_p } \right) } \right) \cdot \left( { \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 19, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 19, 18 } \right) } } \right) \over \left( { { tutorial11.y \left( 20 \right) } - { tutorial11.y \left( 18 \right) } } \right) } \right) } \right) - { tutorial11.Q_t } } = 0$$
True
BC(right)(20,00)
$\mathit{BC(right)(20,00)}$
$${ { \partial { { \left( { T \left( { 20, 0 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 0 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 0 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 0 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,01)
$\mathit{BC(right)(20,01)}$
$${ { \partial { { \left( { T \left( { 20, 1 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 1 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 1 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 1 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,02)
$\mathit{BC(right)(20,02)}$
$${ { \partial { { \left( { T \left( { 20, 2 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 2 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 2 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 2 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,03)
$\mathit{BC(right)(20,03)}$
$${ { \partial { { \left( { T \left( { 20, 3 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 3 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 3 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 3 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,04)
$\mathit{BC(right)(20,04)}$
$${ { \partial { { \left( { T \left( { 20, 4 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 4 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 4 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 4 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,05)
$\mathit{BC(right)(20,05)}$
$${ { \partial { { \left( { T \left( { 20, 5 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 5 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 5 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 5 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,06)
$\mathit{BC(right)(20,06)}$
$${ { \partial { { \left( { T \left( { 20, 6 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 6 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 6 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 6 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,07)
$\mathit{BC(right)(20,07)}$
$${ { \partial { { \left( { T \left( { 20, 7 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 7 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 7 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 7 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,08)
$\mathit{BC(right)(20,08)}$
$${ { \partial { { \left( { T \left( { 20, 8 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 8 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 8 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 8 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,09)
$\mathit{BC(right)(20,09)}$
$${ { \partial { { \left( { T \left( { 20, 9 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 9 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 9 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 9 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,10)
$\mathit{BC(right)(20,10)}$
$${ { \partial { { \left( { T \left( { 20, 10 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 10 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 10 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 10 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,11)
$\mathit{BC(right)(20,11)}$
$${ { \partial { { \left( { T \left( { 20, 11 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 11 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 11 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 11 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,12)
$\mathit{BC(right)(20,12)}$
$${ { \partial { { \left( { T \left( { 20, 12 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 12 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 12 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 12 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,13)
$\mathit{BC(right)(20,13)}$
$${ { \partial { { \left( { T \left( { 20, 13 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 13 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 13 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 13 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,14)
$\mathit{BC(right)(20,14)}$
$${ { \partial { { \left( { T \left( { 20, 14 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 14 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 14 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 14 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,15)
$\mathit{BC(right)(20,15)}$
$${ { \partial { { \left( { T \left( { 20, 15 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 15 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 15 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 15 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,16)
$\mathit{BC(right)(20,16)}$
$${ { \partial { { \left( { T \left( { 20, 16 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 16 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 16 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 16 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,17)
$\mathit{BC(right)(20,17)}$
$${ { \partial { { \left( { T \left( { 20, 17 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 17 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 17 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 17 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,18)
$\mathit{BC(right)(20,18)}$
$${ { \partial { { \left( { T \left( { 20, 18 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 18 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 18 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 18 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,19)
$\mathit{BC(right)(20,19)}$
$${ { \partial { { \left( { T \left( { 20, 19 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 19 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 19 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 19 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True
BC(right)(20,20)
$\mathit{BC(right)(20,20)}$
$${ { \partial { { \left( { T \left( { 20, 20 } \right) } \right) } } } \over { \partial {x} } } = 0$$
$${ \left( { \left( { \left( { {3 {}} \cdot { tutorial11.T \left( { 20, 20 } \right) } } \right) - \left( { {4 {}} \cdot { tutorial11.T \left( { 19, 20 } \right) } } \right) } \right) + { tutorial11.T \left( { 18, 20 } \right) } } \right) \over \left( { { tutorial11.x \left( 20 \right) } - { tutorial11.x \left( 18 \right) } } \right) } = 0$$
True